Formation and order of matrix

Chapter 3 Class 12 Matrices
Concept wise

Let’s consider the matrix

It has 2 rows & 2 columns

So, we write the order as

And,

3, 2, 1, 4 are elements of matrix A

We write the matrix A as

Where

a 11 → element in 1st row, 1st column

a 12 → element in 1st row, 2nd column

a 21 → element in 2nd row, 1st column

a 22 → element in 2nd row, 2nd column

So,

a 11 = 3

a 12 = 2

a 21 = 1

a 22 = 4

For matrix

It has 3 rows & 2 columns

So, the order is 3 × 2.

We write matrix B as

Similarly,

## a ij = i + j

A 4 × 3 matrix looks like

Now,

a 11 = 1 + 1 = 2

a 12 = 1 + 2 = 3

a 13 = 1 + 3 = 4

a 21 = 2 + 1 = 3

a 22 = 2 + 2 = 4

a 23 = 2 + 3 = 5

a 32 = 3 + 2 = 5

a 33 = 3 + 3 = 6

a 41 = 4 + 1 = 5

a 42 = 4 + 2 = 5

a 43 = 4 + 3 = 7

So, our matrix is

### Transcript

A = [β 8(3&2@1&4)] 2 Γ 2 Rows Column And, 3, 2, 1, 4 are elements of matrix A A = [β 8(π_11&π_12@π_21&π_22 )] B = [β 8(3&2@1&4@5&3)] B = [β 8(3&2@1&4@5&3)]_(3 Γ 2) Matrix Order [β 8(9&5&2@1&8&5@3&1&6)] 3 Γ 3 [β 8(1&2&5&8&π₯&π§)] 1 Γ 6 [β 8(5@9@3@π¦@tan^(β1)β‘π₯ )] 5 Γ 1 [β 8(sinβ‘π₯&cosβ‘π₯&tanβ‘π₯&cotβ‘π₯@sinβ‘π¦&cosβ‘π¦&tanβ‘π¦&cotβ‘π¦@sinβ‘π§&cosβ‘π§&tanβ‘π§&cotβ‘π§ )] 3 Γ 4 A = [β 8(π_11&π_12&π_13@π_21&π_22&π_23@π_31&π_32&π_33@π_41&π_42&π_43 )] A = [β 8(2&3&4@3&4&5@4&5&6@5&6&7)] A = [β 8(2&3&4@3&4&5@4&5&6@5&6&7)]